mat237t3 - 1. [8 marks] Find all the critical points of the...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
1. [8 marks] Find all the critical points of the function and ) )( 3 ( ) , ( 2 2 y x x y x f = classify each of them as a local maximum, local minimum, or saddle point. 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2. [8 marks] Suppose the velocity field of a fluid is given by j i F z x + = (in m/sec). Let S be the triangle with vertices (1, 0, 0), (0, 2, 0), (0, 0, 2). How many cubic meters of fluid per second are crossing the surface S in the direction of the upward normal n to S ? ( Recall that the flux of F across S is ) ∫∫ S dS n F 3
Background image of page 2
3. (a) [3 marks] Formulate the Divergence Theorem and all of its assumptions. (b) [7 marks] Evaluate if ∫∫ S dS n F k j i F z y x + + = 4 1 where S is the complete boundary of region } 0 , 1 : ) , , {( 2 2 4 1 2 + + = z z y x z y x V and S is oriented so that the positive normal n points out of the region V . 4
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4. [7 marks] A cyclist rides up a mountain along the path shown in Figure 1. Throughout the trip he exerts a conservative force
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/21/2010 for the course MATHEMATIC MAT237Y1 taught by Professor Romauldstanczak during the Fall '09 term at University of Toronto- Toronto.

Page1 / 8

mat237t3 - 1. [8 marks] Find all the critical points of the...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online